Superconducting charge qubits from a microscopic many-body perspective

The quantised Josephson junction equation that underpins the behaviour of charge qubits and other tunnel devices is usually derived through cannonical quantisation of the classical macroscopic Josephson relations. However, this approach may neglect effects due to the fact that the charge qubit consists of a superconducting island of finite size connected to a large superconductor. We show that the well known quantised Josephson equation can be derived directly and simply from a microscopic many-body Hamiltonian. By choosing the appropriate strong coupling limit we produce a highly simplified Hamiltonian that nevertheless allows us to go beyond the mean field limit and predict further finite-size terms in addition to the basic equation.Comment: Accepted for J Phys Condensed Matte

Generalization of Dirac Non-Linear Electrodynamics, and Spinning Charged Particles

In this note we generalized the Dirac non-linear electrodynamics, by introducing two potentials (namely, the vector potential A and the pseudo-vector potential gamma^5 B of the electromagnetic theory with charges and magnetic monopoles) and by imposing the pseudoscalar part of the product omega.omega* to be zero, with omega = A + gamma^5 B. We show that the field equations of such a theory possess a soliton-like solution which can represent a priori a "charged particle", since it is endowed with a Coulomb field plus the field of a magnetic dipole. The rest energy of the soliton is finite, and the angular momentum stored in its electromagnetic field can be identified --for suitable choices of the parameters-- with the spin of the charged particle. Thus this approach seems to yield a classical model for the charged (spinning) particle, which does not meet the problems met by earlier attempts in the same direction.Comment: standard LaTeX file; 16 pages; it is a corrected version of a paper appeared in Found. Phys. (issue in honour of A.O.Barut) 23 (1993) 46

A Direct Multigrid Poisson Solver for Oct-Tree Adaptive Meshes

We describe a finite-volume method for solving the Poisson equation on oct-tree adaptive meshes using direct solvers for individual mesh blocks. The method is a modified version of the method presented by Huang and Greengard (2000), which works with finite-difference meshes and does not allow for shared boundaries between refined patches. Our algorithm is implemented within the FLASH code framework and makes use of the PARAMESH library, permitting efficient use of parallel computers. We describe the algorithm and present test results that demonstrate its accuracy.Comment: 10 pages, 6 figures, accepted by the Astrophysical Journal; minor revisions in response to referee's comments; added char

Matter-wave solitons with a periodic, piecewise-constant nonlinearity

Motivated by recent proposals of ``collisionally inhomogeneous'' Bose-Einstein condensates (BECs), which have a spatially modulated scattering length, we study the existence and stability properties of bright and dark matter-wave solitons of a BEC characterized by a periodic, piecewise-constant scattering length. We use a ``stitching'' approach to analytically approximate the pertinent solutions of the underlying nonlinear Schr\"odinger equation by matching the wavefunction and its derivatives at the interfaces of the nonlinearity coefficient. To accurately quantify the stability of bright and dark solitons, we adapt general tools from the theory of perturbed Hamiltonian systems. We show that solitons can only exist at the centers of the constant regions of the piecewise-constant nonlinearity. We find both stable and unstable configurations for bright solitons and show that all dark solitons are unstable, with different instability mechanisms that depend on the soliton location. We corroborate our analytical results with numerical computations.Comment: 16 pages, 7 figures (some with multiple parts), to appear in Physical Review

Solid Freeform Fabrication of Functional Silicon Nitride Ceramics by Laminated Object Manufacturing 1

The processing of silicon nitride (Si3N4) structural ceramics by Laminated Object Manufacturing (LOM) using ceramic tape preforms was investigated. The key processing stages involved green shape formation (which used the LOM process), followed by the burnout of all organics, and final densification by pressureless sintering. Two material systems were considered. These were a) monolithic Si3N4 and b) a preceramic polymer infiltrated Si3N4. The raw materials for the process were tape preforms of Si3N4, which were fabricated by standard tape casting techniques. Mechanical property data obtained for the LOM processed Si3N4 showed high strength and fracture toughness values. The room temperature and high temperature (1260 o C) flexural strengths were in the range of 700-900 MPa and 360-400 MPa, respectively. The fracture toughness averaged from 5.5-7.5 MPa.m1/2. These strength and fracture toughness values are comparable to those reported for conventionally prepared Si3N4 ceramics. Thus, this research demonstrated that the LOM technique is a viable method for preparing functional Si3N4 ceramics with good physical and mechanical properties.Mechanical Engineerin